Tottenham's Aaron Lennon, Jermain Defoe and Andros Townsend all appeared to be the subject of racist chanting during last night's 0-0 draw against the Italian side at White Hart Lane.
UEFA, whose president Michel Platini was at the game, are awaiting reports from the match delegate and referee Ovidiu Alin Hategan before deciding to take action against Lazio.
Members of anti-discrimination group Football Against Racism in Europe (FARE) who were in the crowd at the north London ground, said they heard monkey chanting and they are now filing their reports to UEFA to help them with any potential disciplinary action.
The group's executive director Powar thinks European football's governing body need to issue a tough punishment on Lazio to send a strong message to the club that racism will not be tolerated.
He said: "UEFA normally operate a 'three strikes and you're out' policy, and I think Lazio are at first base in that respect, but if (UEFA) really want to set the bar high, if they really want to send out a strong message, then I think they can do so regardless of whether it's a first or second offence.
"I therefore think that UEFA could move directly to something like a match behind closed doors (punishment).
"They could suspend that punishment, perhaps, and then if something happens further down the line, then they can trigger that.
"Lazio are a strong club. They have been part of the European football scene for a long time. There needs to be quite a hard symbolic action taken when these instances occur.
"This punishment is one way of waking the club and the fans up to some of the problems that they face."
Last season UEFA fined Porto £16,700 for their fans' racist abuse at Mario Balotelli and Yaya Toure, but then caused outrage by fining Manchester City £24,735 for being one minute late back onto the pitch after half-time during the Europa League clash.
The punishment also seemed small fry compared to the £80,000 sanction they handed down to Nicklas Bendtner for revealing a sponsor's logo on his underpants during Euro 2012.
Powar urged Spurs to put pressure on UEFA by submitting an official complaint against the Italian side, who they play in the reverse fixture in November.
"It is important that Tottenham raise their concerns with UEFA directly," Powar added.
"It carries a certain weight if matters are passed on to them by club officials - a weight that regular fans cannot match.
"All too often in the past, there have been clubs - not necessarily Tottenham - who are concerned with the diplomacy of international football, perhaps mindful that they have to play these opponents again.
"But this seems to be a fairly clear situation where fans have come to White Hart Lane and insulted some of the Tottenham players.
"There is the potential for flashpoints in the return game in Rome and UEFA need to be aware of that."
Tottenham manager Andre Villas-Boas said last night that he did not hear the chants and that he was happy for UEFA to deal with the matter.
Some sections of Lazio's fan-base have long been synonymous with the far right in Italy.
Their former striker Paolo di Canio famously made a fascist salute to the club's fans after the Rome derby in 2005 and caused outrage in his autobiography by claiming former Italian dictator Benito Mussolini was a "very principled, ethical individual".
Powar, who fears there could be more trouble in the return fixture, also claims Lazio fans were making illegal salutes at Liverpool Street station prior to last night's game.
"We have also had a report that Lazio fans were making what they called a Roman salute at Liverpool Street station," he said.
"Most of us know the Roman salute is more or less a Sieg Heil really.
"To do that before the game, in a very public place, is unlawful in this country. It is an incitement to racial hatred."
Barclays Premier League managers united on Friday to call for tough action against racism from the terraces.
Arsenal boss Arsene Wenger said: "How we improve things is by being absolutely resilient to fight against stupidity. It looks like it will be an endless fight but we have to fight against it, against stupid reactions from the crowd and I'm certain we have to be tougher at every level."
Aston Villa manager Paul Lambert said: "It's not right. There's no place for it in any walk of life, let alone football.
"Hopefully UEFA can do something about it. You'll still get a minority of idiots out there who do it, but there's no place for it."